MatematikA.DifferentiationAfSammensatFunktion History

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June 11, 2013, at 11:51 PM by 31.25.19.69 -
Changed lines 15-16 from:

{$$\left( f(g(x)) \right)'= f'(g(x)) \cdot g'(x)$$}

to:

{$$f(g(x))'= f'(g(x)) \cdot g'(x)$$}

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June 11, 2013, at 11:50 PM by 31.25.19.69 -
Added line 4:
Changed lines 15-16 from:

{$$\left( f(x) \cdot g(x)\right)'= f'(x)\cdot g(x)+f(x)\cdot g'(x)$$}

to:

{$$\left( f(g(x)) \right)'= f'(g(x)) \cdot g'(x)$$}

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(:toggle div=produktbevis init=show button=1 lshow=Bevis lhide="Skjul Bevis":)

to:

(:toggle div=sammensatbevis init=show button=1 lshow=Bevis lhide="Skjul Bevis":)

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June 11, 2013, at 11:48 PM by 31.25.19.69 -
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Differentiation af sammensat funktion

Formel for differentiation af en sammensat funktion:

(:table border=1 width=40% cellpadding=10 align=center bgcolor=#cccc99 cellspacing=0 :) (:cellnr:) En sammensat funktion {$\displaystyle f(g(x))$}, hvor {$f(x)$} og {$g(x)$} er differentiable funktioner, differentieres på følgende måde:


{$$\left( f(x) \cdot g(x)\right)'= f'(x)\cdot g(x)+f(x)\cdot g'(x)$$}

(:tableend:)

(:toggle div=produktbevis init=show button=1 lshow=Bevis lhide="Skjul Bevis":)

Bevis:

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